Journal of the Ramanujan Mathematical Society

Volume 39, Issue 3, September 2024 pp. 211–217.

On Gao-Thangadurai's conjecture

Authors: Umesh Shankar, Srilakshmi Krishnamoorty and Karthikesh Baskaran
Author institution:Department of Mathematics, Indian Institute of Technology, Bombay, Mumbai 400 076, India.

Summary: Let G be a finite abelian group. Let g(G) be the smallest positive integer t such that every subset of cardinality t of the group G contains a subset of cardinality exp(G) whose sum is zero. In this paper, we show that if X is a subset of ℤ{2}{2n} with cardinality 4n+1 and 2n or 2n−1 elements of X have the same first coordinates, then X contains a zero sum subset. As an application of our results we prove that g(ℤ{2}{6}) = 13. This settles Gao-Thangadurai's conjecture for the case n = 6. We also prove some results which can be used to prove the general even n cases of the conjecture.

Contents Full-Text PDF